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 i don't think the people who came up with the idea of PoW on notes really understood what they were getting into

it's not fit for this use case

do some research into bitmessage and you probably will find several reasons why it failed

spammers will set up ASICs to win proofs before you can say "boo" 
 I think I read something earlier how ASICs can't be setup to 'break' single SHA256 calculations. Could be dead wrong though. 
 most asic protocols are built around sending the 80 byte stream so that is a bit of a limitation, but it's firmware, really it only depends on whether the onboard embedded processor can cope with note sized data blobs to hash on

i'd guess they are implemented as sponge functions so probably yes

in most cases it will require a firmware change but i think that probably GPUs are fast enough to render the rest of users out of the game anyway 
 probably some can be modified but it is likely the chips are hard baked to take 80 byte inputs 
 i should add that definitely a lot of older ones with less grunt won't be because not all SHA256 altcoins had 80 byte long block headers

many of them sit idle, uneconomic as anything but a resistave heat element in all seriousness, but this could spawn a new value to chase with them

Proof of Work: leave it to the bitcoin chain and forget any other use of it

the economics of proof of work are like bitcoin itself: there can be only one

more than one target to use it on and the hashpower will dance the tango on your protocol